Metaheuristic scheduling benchmarks and a transparent SWARA–WASPAS decision study for flexible manufacturing systems

Introduction

FMS planning is inherently a multilevel optimization problem. At the operational level, schedules must allocate work to shared resources under combinatorial complexity. At the strategic level, designers must select machine counts, trans-porter capacity, buffering, and flexibility levels while balancing cost against multiple performance criteria. Solving only one of these layers is insufficient: strong scheduling on a poor configuration remains limited, while a good configuration without effective scheduling leaves value unrealized. The optimization literature offers many heuristics for FMS loading and scheduling, including genetic algorithms, evolutionary methods, and hybrid search procedures [1,3] . Simulated annealing also remains attractive because of its principled escape from local minima through probabilistic uphill moves [4,5] . Meanwhile, Multi-Criteria Decision-Making (MCDM) methods such as SWARA and WASPS have become useful in manufacturing selection problems where cost, through put, and responsiveness must be considered simultaneously [6,9] . This paper combines these viewpoints through two linked but methodologically distinct studies. The first benchmarks met heuristic scheduling quality across increasing problem sizes. The second ranks candidate FMS configurations using a transparent SWARA-WASPAS model and tests the stability of the ranking over multiple λ values. The paper makes the following contributions. 1. It provides a size-dependent empirical comparison of GA, DE, and SA on common FMS Scheduling benchmarks. 2. It defines the optimization objective explicitly as makes pan and documents the benchmark instance structure.

3. It provides a fully stated SWARA-WASPAS decision stage, including the surrogate configuration model, normalization rule, criterion weights, and corrected ranking outputs.

Related work

Early FMS research established scheduling and control as central operations-research problems [10] . Genetic algorithms have been widely used for machine loading and sequencing because they can navigate discrete solution spaces effectively [1, 11] . Differential evolution has shown strong global search behavior in continuous optimization and has also been adapted to FMS scheduling [3,12] . Simulated annealing remains relevant because its acceptance mechanism can reduce premature convergence on rugged landscapes [4,13] . On the decision side, SWARA provides a structured approach for deriving criterion weights, while WASPAS blends weighted-sum and weighted-product reasoning to rank alternatives [6,7] . Applications in manufacturing have shown that WASPAS can discriminate among alternatives that are difficult to compare by throughput or cost alone [8] . However, fewer studies integrate a scheduling benchmark and a strategic MCDM layer within a common FMS study. This paper addresses that gap while explicitly separating the optimization benchmark from the surrogate-based decision layer and by avoiding claims of full pipeline integration that are not supported by the experimental design.

Two-stage framework A. Stage1: scheduling benchmark

Three met heuristics are compared: GA with population 50 and 50 generations.

• DE with population 50 and 101 generations.

• SA with 181 iteration sundera cooling schedule. Each algorithm is run independently 50 times on small, medium, and large scheduling instances. The objective is makes pan, defined as Where Cj s the completion time of job j. Lower fitness therefore indicates a shorter overall schedule. The benchmark instances contain 5 job son 3 machines (small),10jobson 5 machines (medium), and 20 jobs on 8 machines (large).Each job contains 3-5 operations, and each operation can be processed on 1-3 capable machines with machine-dependent processing times.

B. Stage2: configuration ranking

Fifteen candidate FMS configurations are evaluated on throughput, utilization, cycle time, work-in-process, and cost. The second stage is a decision-layer study rather than a full DES rerun: candidate configurations are produced from a reproducible surrogate generator with random seed 42. For configuration i with machine count mi, AGV count ai, buffer size bi, AGV speed VI, routing flexibility fi, and independent uncertainty multipliers ξ kU (0.9, 1.1), the surrogate metrics are SWARA is used to define criterion weights and WASPAS is used to rank alternatives. Benefit criteria are normalized by xi j / math sf ma xi xi j and cost criteria by min iX ij / Xi j . . For alternative i, the WASPAS score is computed by blending the weighted-sum and weighted-product models:

Robustness is assessed over λ∈ {0, 0.25,0.5,0.75,1.0}. During manuscript revision, the ranking stage was rechecked and the score-to-alternative mapping was corrected so that the reported results align with the original alternatives rather than with an internally sorted WASPAS output. The resulting ranking should therefore be read as a transparent surrogatebased decision study, not as a final simulation-validated capacity selection result.

B. Interpretation

The performance gap suggests that larger FMS scheduling instances have a rugged search landscape with more local minima. SA benefits from its probabilistic acceptance rule, which permits temporary worsening moves and therefore helps selection result. The search leave local basins. Population-based search remains competitive, but the present benchmark indicates that GA and DE degrade more quickly as complexity increases. The computational cost of SA is higher, but the absolute running time remains modest even for the largest instance. This makes SA attractive for offline scheduling, rescheduling between shifts, or scenario analysis where solution quality dominates sub-second time savings.

B. Rank robustness

The corrected ranking result is unusually stable. Config 11 remains first for every tested λ value, and the top six configurations retain their exact ordinal positions across the full additive-multiplicative blending range. Table IV shows the score trajectory of Config 11. This result matters because MCDM methods are often criticized for sensitivity to weighting assumptions. In the present case, the chosen design remains dominant under both the weighted-product and weighted-sum extremes.

C. Why config 11 wins

The winning configuration has eight machines, one AGV, buffer size 20, AGV speed 1.54 m/s, and routing flexibility 0.9.It does not have the lowest cost, but it combines very high through put (292.64),the best or near-best utilization among the top candidates (0.704), and the shortest cycle time in the top two (12.86). This profile aligns with the SWARA weights in Table I, which strongly favor through put and utilization and assign relatively low weight to cost. This interpretation is conditional on both the stated weight structure and the surrogate equations used to generate the decision alternatives. This finding is valuable because it warns against overreliance on a single KPI. A configuration with extremely high throughput can still lose if it sacrifices utilization, cycle time, or normalized cost performance. By considering multiple criteria simultaneously, the decision model favors structurally strong, high-output alternatives that remain efficient after normalization rather than one-dimensional extermination.

Planning implications

The two studies are complementary rather than fully coupled. The scheduling benchmark shows that algorithm choice should depend on problem size: GA is attractive when speed dominates, DE remains viable on small search spaces, and SA should be preferred as complexity increases. The MCDM study then addresses a different planning question: under an explicitly stated surrogate decision model and weight structure, which structural design would be preferred? Taken together, the results suggest the following policy for FMS projects. 1) Use SA as the primary optimizer for medium and large offline scheduling instances.

2) Reserve GA for rapid approximate schedules when speed is more important than final quality.

3) Do not select strategic configurations on throughput alone; rank those using a multi-criteria model with published weights and normalization rules. 4) When cost is intentionally assigned a low decision weight, expect capacity-intensive, high-through put alter-natives to dominate the final ranking.

Conclusion

This paper presented a Meta heuristic scheduling benchmark together with a transparent SWARA-WASPAS decision study for FMS planning. At the operational level, Meta heuristic scheduling experiments showed that SA scales more favorably than GA and DE as problem complexity grows, achieving the best mean and best observed large-instance make span values. At the strategic level, a corrected SWARA-WASPAS analysis identified Config 11 as the consistently top-ranked surrogate configuration across all tested λ values within the stated decision model. The main contribution is the combination of an operational benchmark and a fully stated decision-model specification in a form suitable for standalone FMS planning studies. Future research should couple the two studies more tightly by using simulation-derived alternatives instead of surrogate-generated ones, incorporating stochastic breakdown scenarios directly into the ranking stage, and testing hybrid Metaheuristics for dynamic rescheduling.

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